A triple product convolver is a device that consists of a tapped delay line with multipliers on each tap and a summing junction, see FIG. 1. The output signal at any instant of time is proportional to the product of chirp signals 1 and 2 signals S.sub.1, S.sub.2, . . . , S.sub.n. This configuration of multipliers and nonlinear elements operatively coupled to a tapped delay line is highly useful in calculating Fourier transforms or for signal beamforming.
A recurring problem confronting designers of convolvers became apparent in the quality of the multipliers' output signals, namely, the problems associated with nonlinearity of signals over a wide dynamic range comprised the convolvers effectiveness. One apparatus and method used to perform the required multiplications use a bipolar transistor in the common base mode as noted in FIG. 2. The output signal is a function of the product of v.sub.RF and I.sub.E where I.sub.E R.sub.E +V.sub.T ln [I.sub.E /I.sub.ES +1]=V.sub.E however, v.sub.o is nonlinear function of V.sub.E, the modulation signal. To achieve an accurate triple product convolution, v.sub.o must vary linearly with V.sub.E. To linearize the functional relationship between v.sub.o and V.sub.E, the emitter resistance R.sub.E must be large (about 100 kilohms). This however, reduces the frequency response of the V.sub.E terminal due to the emitter-base capacitance of the transistor. Consequently, this circuit has demonstrated that it is not suitable for linear, high frequency modulation signals which are normally among the signals being processed in fast triple product convolvers.
A variation of a multiplier is depicted in FIG. 3 wherein a dual gate field effect transistor is included in the multiplier. The output signal v.sub.o is a function of the product of v.sub.RF with V.sub.MOD ; however, this circuit is linear over a vary limited dynamic range which is typically 15 to 20 db. In addition, there is a rather large variation in the phase of v.sub.o with respect to v.sub.RF as V.sub.MOD varies. The phase variation is unacceptable for beamforming systems as well as systems for calculating Fourier transforms since their proper operation depends on accurate summing of signals with a precise phase relationship.
Thus, there is a continuing need in the state of the art for a variable transconductance multiplier having a substantially linear response over a wide dynamic range to enhance the performance of vast triple product convolvers.